Work

The on/off Brownian snake

Year: 2026

Type: preprint

Abstract: We define what we call an on/off Brownian snake. We use this to construct on/off super Brownian motion recently introduced to the literature by Blath and Jacobi and which is a measure-valued branching process with a dormant state and an active state. Our construction mirrors the construction of super Brownian motion from the Brownian snake by Le Gall. We use the on/off Brownian snake to obtain results concerning the support, range, and expected total mass of on/off super Brownian motion.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.01852

Authors: Buckland, Matthew, Jacobi, Dave

Institutions: University of Warwick, Technische Universität Berlin

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Warwick, University of Oxford, Deutsche Forschungsgemeinschaft, Universität zu Lübeck, Engineering and Physical Sciences Research Council

Awards: G1372115314, G1600321425, G1875930355, G2033548659, G2596867474, Stochastische Prozesse in der Evolution von Parasiten, Anomalous diffusion via self-interaction and reflection, G60923575, EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation, EXC 2046: MATH+: Berlin Mathematics Research Center

OpenAlex ID: W7148868284

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